Question: Solve for $n$. $2-\dfrac12n=3n+16$ $n=$
Explanation: We need to manipulate the equation to get $ n $ by itself. $\begin{aligned} 2-\dfrac12n&=3n+16 \\\\ 2-\dfrac12n {-3n} &= 3n+16{-3n} &&\gray{\text{Subtract 3n from each side.}}\\\\ -\dfrac72n+2&=16 &&\gray{\text{Combine like terms.}}\\\\ -\dfrac72n+2{-2} &= 16{-2} &&\gray{\text{Subtract 2 from each side.}}\\\\ -\dfrac72n &=14 &&\gray{\text{Combine like terms.}}\\\\ -\dfrac72n\cdot\left({-\dfrac27}\right) &= 14\cdot\left({-\dfrac27}\right) &&\gray{\text{Multiply each side by }-\dfrac27.}\\\\ n&=-\dfrac{28}7\\\\ n &= {-4} &&\gray{\text{Simplify.}}\\\\ \end{aligned}$ The answer: $ n= { -4 }~~~~~~~~$ [Let's check our work!]